Answer the following questions inside the 2 shaded box. Examples are given.

Activity 13: April 6&8, 2021 Complete the table and predict profit assuming sales of P20 million (in millions) (in millions) Profit Sales 5 18 19 13 23 24 5.5 16E. Trend Line Forecast Yrma+ bt Where: Y1 = Forecast for period t a = Value of Y, @ t= 0 6 |Page b = slope of the line t = specified number of time periods from t = 0 b= nEty- Et Zy nEtz-(Et) Ey- b Et n where n = number of periods y= value of the time series Example: predict the sales for period 11 and 12 Week(t) Unit sales (y) ty 1 800 1 800 810 4 1,620 3 830 9 2,490 820 16 3,280 5 850 25 4.250 6 810 36 4,860 825 49 5,775 840 64 6,720 805 81 7,425 10 830 100 8,300 It = 55 Ey = 8220 Etz = 385 Ety = 45,340 b= 10 (45,340)-(55) (8,220) 1.60 10 (385)-(55) 8220-1.60 (55) = 813 10 Y, = a + bt Y, = a + bt =813 + 1.60 (11) =813 + 1.60 (12) = 831 units = 832 units Activity 12: Complete the table and predict sales for period 11. Formulas and solutions are not required Week(t) Unit sales (y) ty 820 800 825 815 835 825 810 800 830 840F. Simple Linear Regression Involves a linear relationship between two variables Yx = a + bx Where: Yx = Predicted ( dependent) variable x = Predictor (independent) variable a = Value of Yx @ x =0 b = slope of the line nExy- Ex Ey b= nEx-(Ex) Ey- b Ex n where n = number of observations Example JC Hamburgers has chain of 10 stores in Southern Leyte. Sales figures and profit for the stores are given in the following table. Predict profit for a store assuming sales of P30 million. ( in millions) (in millions) Sales ( x ) Profit (v) xy 15 8 225 120 17 9 289 153 21 13 441 273 18 10 324 180 19 11 361 209 22 14 484 308 16 8.5 256 136 17 10 289 170 25 15 625 375 20 13 400 260 Ex =190 Ey =111.5 Ex '=3694 Exy = 2184 nExy- ExZy 10 (2,184)-(190) (111.5) b= nEx-(Ex)2 10 (3,694)-(190)2 =.78 Ey- b Ex 111.5-(.78) (190) a = =-3.67 n 10 y =a+bx =-3.67 + (.78) (30) = 19.73 profit of P19,730,000 if sales is P30,000,000